en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+y)^{20}

Solution

expand

(x + y)^{20}

Solution

x^{20} + 20 x^{19} y + 190 x^{18} y^{2} + 1140 x^{17} y^{3} + 4845 x^{16} y^{4} + 15504 x^{15} y^{5} + 38760 x^{14} y^{6} + 77520 x^{13} y^{7} + 125970 x^{12} y^{8} + 167960 x^{11} y^{9} + 184756 x^{10} y^{10} + 167960 x^{9} y^{11} + 125970 x^{8} y^{12} + 77520 x^{7} y^{13} + 38760 x^{6} y^{14} + 15504 x^{5} y^{15} + 4845 x^{4} y^{16} + 1140 x^{3} y^{17} + 190 x^{2} y^{18} + 20 x y^{19} + y^{20}

Solution steps

(x + y)^{20}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = y

= i = 0 \sum 20 (i 20) x^{(20 - i)} y^{i}

Expand summation

= \frac{20 !}{0 ! ( 20 - 0 ) !} x^{20} y^{0} + \frac{20 !}{1 ! ( 20 - 1 ) !} x^{19} y^{1} + \frac{20 !}{2 ! ( 20 - 2 ) !} x^{18} y^{2} + \frac{20 !}{3 ! ( 20 - 3 ) !} x^{17} y^{3} + \frac{20 !}{4 ! ( 20 - 4 ) !} x^{16} y^{4} + \frac{20 !}{5 ! ( 20 - 5 ) !} x^{15} y^{5} + \frac{20 !}{6 ! ( 20 - 6 ) !} x^{14} y^{6} + \frac{20 !}{7 ! ( 20 - 7 ) !} x^{13} y^{7} + \frac{20 !}{8 ! ( 20 - 8 ) !} x^{12} y^{8} + \frac{20 !}{9 ! ( 20 - 9 ) !} x^{11} y^{9} + \frac{20 !}{10 ! ( 20 - 10 ) !} x^{10} y^{10} + \frac{20 !}{11 ! ( 20 - 11 ) !} x^{9} y^{11} + \frac{20 !}{12 ! ( 20 - 12 ) !} x^{8} y^{12} + \frac{20 !}{13 ! ( 20 - 13 ) !} x^{7} y^{13} + \frac{20 !}{14 ! ( 20 - 14 ) !} x^{6} y^{14} + \frac{20 !}{15 ! ( 20 - 15 ) !} x^{5} y^{15} + \frac{20 !}{16 ! ( 20 - 16 ) !} x^{4} y^{16} + \frac{20 !}{17 ! ( 20 - 17 ) !} x^{3} y^{17} + \frac{20 !}{18 ! ( 20 - 18 ) !} x^{2} y^{18} + \frac{20 !}{19 ! ( 20 - 19 ) !} x^{1} y^{19} + \frac{20 !}{20 ! ( 20 - 20 ) !} x^{0} y^{20}

Simplify

\frac{20 !}{0 ! ( 20 - 0 ) !} x^{20} y^{0} : x^{20}

Simplify

\frac{20 !}{1 ! ( 20 - 1 ) !} x^{19} y^{1} : 20 x^{19} y

Simplify

\frac{20 !}{2 ! ( 20 - 2 ) !} x^{18} y^{2} : 190 x^{18} y^{2}

Simplify

\frac{20 !}{3 ! ( 20 - 3 ) !} x^{17} y^{3} : 1140 x^{17} y^{3}

Simplify

\frac{20 !}{4 ! ( 20 - 4 ) !} x^{16} y^{4} : 4845 x^{16} y^{4}

Simplify

\frac{20 !}{5 ! ( 20 - 5 ) !} x^{15} y^{5} : 15504 x^{15} y^{5}

Simplify

\frac{20 !}{6 ! ( 20 - 6 ) !} x^{14} y^{6} : 38760 x^{14} y^{6}

Simplify

\frac{20 !}{7 ! ( 20 - 7 ) !} x^{13} y^{7} : 77520 x^{13} y^{7}

Simplify

\frac{20 !}{8 ! ( 20 - 8 ) !} x^{12} y^{8} : 125970 x^{12} y^{8}

Simplify

\frac{20 !}{9 ! ( 20 - 9 ) !} x^{11} y^{9} : 167960 x^{11} y^{9}

Simplify

\frac{20 !}{10 ! ( 20 - 10 ) !} x^{10} y^{10} : 184756 x^{10} y^{10}

Simplify

\frac{20 !}{11 ! ( 20 - 11 ) !} x^{9} y^{11} : 167960 x^{9} y^{11}

Simplify

\frac{20 !}{12 ! ( 20 - 12 ) !} x^{8} y^{12} : 125970 x^{8} y^{12}

Simplify

\frac{20 !}{13 ! ( 20 - 13 ) !} x^{7} y^{13} : 77520 x^{7} y^{13}

Simplify

\frac{20 !}{14 ! ( 20 - 14 ) !} x^{6} y^{14} : 38760 x^{6} y^{14}

Simplify

\frac{20 !}{15 ! ( 20 - 15 ) !} x^{5} y^{15} : 15504 x^{5} y^{15}

Simplify

\frac{20 !}{16 ! ( 20 - 16 ) !} x^{4} y^{16} : 4845 x^{4} y^{16}

Simplify

\frac{20 !}{17 ! ( 20 - 17 ) !} x^{3} y^{17} : 1140 x^{3} y^{17}

Simplify

\frac{20 !}{18 ! ( 20 - 18 ) !} x^{2} y^{18} : 190 x^{2} y^{18}

Simplify

\frac{20 !}{19 ! ( 20 - 19 ) !} x^{1} y^{19} : 20 x y^{19}

Simplify

\frac{20 !}{20 ! ( 20 - 20 ) !} x^{0} y^{20} : y^{20}

= x^{20} + 20 x^{19} y + 190 x^{18} y^{2} + 1140 x^{17} y^{3} + 4845 x^{16} y^{4} + 15504 x^{15} y^{5} + 38760 x^{14} y^{6} + 77520 x^{13} y^{7} + 125970 x^{12} y^{8} + 167960 x^{11} y^{9} + 184756 x^{10} y^{10} + 167960 x^{9} y^{11} + 125970 x^{8} y^{12} + 77520 x^{7} y^{13} + 38760 x^{6} y^{14} + 15504 x^{5} y^{15} + 4845 x^{4} y^{16} + 1140 x^{3} y^{17} + 190 x^{2} y^{18} + 20 x y^{19} + y^{20}

Popular Examples

simplify 1^{1/n}simplify

1^{\frac{1}{n}}

simplify 1-2sin^2(a)simplify

1 - 2 sin^{2} (a)

simplify ((a-1)/a)^6 simplify

(\frac{a - 1}{a})^{6}

simplify (x^2-1)^2+8x(x^2+1)+19x^2 simplify

(x^{2} - 1)^{2} + 8 x (x^{2} + 1) + 19 x^{2}

simplify x^2+2x-2/25 x-2 simplify

x^{2} + 2 x - \frac{2}{25} x - 2

Frequently Asked Questions (FAQ)

What is expand (x+y)^{20} ?
The solution to expand (x+y)^{20} is